**N connected spring in vertical direction (with gravity)**

Created by prof Hwang Modified by Ahmed

Original project N connected spring in vertical direction (with gravity)

This center spring in this applet simulate the above situation.

The spring force where is the equilibrium position.

The damping force is assumed to be , where b is the damping constant.

In the following there are n springs in the simulation, the mass at two ends only experience one force from the spring.

Howerer, the other particles in between experience two forces from two springs at different side.

For the nth particle (n!=0 and n!=N-1), where N is the total number of the spring

Assume y for the n-th particle is y_n,

The n-th sprint force F_n =-k (y_{n}-y_{n+1}-L_0) -k (y_{n-1}-y_{n}-L_0)= k(2y_n- y_{n+1}-y_{n-1})

If you unchecked the fixed checkbox, the center spring will be released and fall down.

You can adjust b value, adjust mass or spring constant to find new equilibrium positions.

You can drag any particles up/down, too!

uncheck fixed checkbox and click play to find the answer to the above question.

**Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.**This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

- Please feel free to post your ideas about how to use the simulation for better teaching and learning.
- Post questions to be asked to help students to think, to explore.
- Upload worksheets as attached files to share with more users.